Van Dijk signed for the Reds last month for a record £75m from Southampton.
Carragher said, "I think it will prove to be a great signing, but he hasn't hit the ground running.
"I think he needs to get fit and lose a bit of weight. He actually looks too big. Maybe that's to do with not having a pre-season."
Carragher also supported the decision to allow Daniel Sturridge to leave on-loan for West Brom.
"I don't think it's a problem letting Sturridge go," Carragher says. "I actually think he was falling down the pecking order, below Solanke. Are Solanke and Ings good enough as back-up for Liverpool? No. But that's got nothing to do with Sturridge leaving.
"We always go back to the season where Liverpool nearly won the league, but that's not the Daniel Sturridge we see today. There's a reason Daniel Sturridge has gone to West Brom. They're bottom of the league and that's where he's ended up unfortunately for his career.
"When he was on form, when he was fit, he was one of the best strikers in England, maybe the best striker in England at that time. But that's three or four years ago, he's a different player now."